A generalized regionalization framework for geographical modelling and its application in spatial regression. (arXiv:2206.09429v2 [stat.ME] UPDATED)
Models applied to geographic data face a trade-off between producing general
results and capturing local variations due to spatial heterogeneity. Spatial
modelling within carefully defined regions offers an intermediate position
between global and local models. However, current spatial optimization
approaches to delineate homogeneous regions consider the similarity of
attribute values, thus unable to identify regions with similar data generation
processes described by geographical models. We propose a generalized
regionalization framework, which optimizes region delineation corresponding to
a model with region-specific parameters. Within this framework, we introduce
three regionalization algorithms, namely automatic zoning procedure (AZP),
K-Models, and Regional-K-Models. We adopt an objective function that jointly
minimizes modelling errors and the complexity of the region scheme. Results
from regression experiments indicate that the K-Models algorithm reconstructs
the regions better than the baseline, according to Rand index and mutual
information measures. Our suggested framework contributes to better capturing
processes exhibiting spatial heterogeneity and may be applied to a wide range
of modelling scenarios.
( 2
min )